## 2. Radio spectral data and separation methodWe have carried out a literature search in order to collect all integrated radio flux densities of Shapley-Ames galaxies at various wavelengths. All flux densities from the literature were scaled to the calibration scale of Baars et al. (1977). Because of the increasing amount of the thermal fraction in the high-frequency part of the radio spectrum the data quality of the high-frequency data is important. Hence, we used only those galaxies where the relative flux density error at 2.8 cm as given in Paper I is below 15 %. In order to increase the statistical significance, all galaxies with flux densities at only three or less frequencies above 400 MHz were eliminated. This lower frequency limit was used to avoid effects of ionization and adiabatic losses of the relativistic electrons. These losses can significantly flatten a radio spectrum in the low-frequency part (e.g. Lerche & Schlickeiser 1982). The remaining sample consists of 74 galaxies. First of all, a rough estimate of the spectral index was made. Then, using this estimated value, flux densities in narrow frequency bands (e.g. 1400 to 1490 MHz or 10.55 to 10.7 GHz) were scaled to an average frequency. The weighted mean of these scaled flux densities was then computed. The weighting factor was the inverse of the squared flux density error. This turned out to yield more reliable fit results compared to using the individual flux densities at slightly different frequencies. We fitted the following model to the mean integrated radio spectra: The first term on the right hand side of Eq. 1 describes the fractional thermal amount of the emission, the second one the synchrotron component. The used frequency dependences hold for the case of optically thin emission, an assumption which for the diffuse disk emission is valid. Furthermore, the model assumes that the synchrotron luminosity can be described by a single power-law. A more detailed discussion of Eq. 1 and its implications can be found in Duric et al. (1988). The assumption on the power-law nature of the non-thermal emission is valid if synchrotron and inverse Compton losses are not very strong and if galaxies do not show core emission. The curvature of a non-thermal radio spectrum with energy losses in the range of normal spiral galaxies is only slight (Condon 1992). Additionally, subtraction of thermal radio flux densities from the composite spectra yields in most cases a power-law or a concave residual spectrum indicating that energy losses have not affected the synchrotron spectra significantly. This will be discussed in more detail in Sect. 4. According to Paper I dominant radio emission from the nucleus is emitted only by galaxies of type Sa and Sab. The diffuse disk emission dominates the total emission for galaxies of later types. Therefore, we expect core emission to be important for less than 10% of our sample. The normalization frequency is . Hence, there are two free parameters to fit: the thermal amount at 1 GHz and the non-thermal spectral index . The best-fit parameters were derived by minimizing the -function. Fig. 1 shows 10 representative examples for galaxies with separated thermal and non-thermal radio emission. Two diagrams are plotted for each galaxy. The left graph shows the mean integrated spectrum, and the solid line represents the fitted spectrum using the best-fit parameters given in the third and fourth column of Table 1. The black area in the right diagrams represents the 1- confidence range of the fitted parameters. The border of this area is given by pairs of and , where the -function has a value of . is the -value of the best-fit parameter and the factor 2.3 is given by Lampton et al. (1976) for the 1- confidence range in case of a two-dimensional parameter space. One can see that the size of this area is mainly determined by the number of data points. The more flux densites are known, the better the fit parameters are determined.
In Table 1 we have compiled the results of the separation for all 74 galaxies. The names of the galaxies and their morphological types are given in the first two columns. The best-fit parameters and are presented in Columns 3 and 4. The errors in and correspond to the 1- confidence interval at fixed and , respectively. In some cases the -fitting method yields the smallest -value for . For such galaxies only upper limits to the thermal fraction are given. These correspond to the lower right border of the confidence region, i.e. the largest values of which fall in the 1- confidence area (e.g. NGC 5054 in Fig. 1). In these cases Column 4 contains the allowed range of from to the upper limit in . The fifth column shows the extrapolated thermal fraction at 10 GHz . The minimum -value is given in Column 6. The seventh column presents the number of degrees of freedom in the fit. The number of data points is reduced by one because of the normalization, and by two because of the two fit parameters. This gives . In the last column the references to the flux densities are listed. © European Southern Observatory (ESO) 1997 Online publication: June 30, 1998 |